We construct supersymmetric black holes with rotation or NUT charge for the
CPn- and the t3 model of N=2, D=4U(1) FI-gauged supergravity. The solutions preserve 2 real
supercharges, which are doubled for their near-horizon geometry. For the
CPn model we also present a generalization to the
nonextremal case, which turns out to be characterized by a
Carter-Pleba\'nski-type metric, and has n+3 independent parameters,
corresponding to mass, angular momentum as well as n+1 magnetic charges. We
discuss the thermodynamics of these solutions, obtain a Christodoulou-Ruffini
mass formula, and shew that they obey a first law of thermodynamics and that
the product of horizon areas depends on the angular momentum and the magnetic
charges only. At least some of the BPS black holes that we obtain may become
instrumental for future microscopic entropy computations involving a
supersymmetric index.Comment: 34 pages, uses jheppub.sty. Final version to appear in JHE